The control of light-matter interaction in complex dielectrics without translational invariance offers great potential for the creation and manipulation of light states.
Complex dielectrics are dielectric structures in which the refractive index varies over length scales comparable to the wavelength of light. In disordered materials, light waves undergo a multiple scattering process and are subject to interference effects leading to Anderson light localization. One of the first phenomena studied in this context was coherent backscattering or weak localization of light. Multiple light scattering in disordered dielectrics shows many similarities with the propagation of electrons in semiconductors, and various phenomena that are known for electron transport also appear to have their counterpart in optics. Important examples are the optical Hall effect and optical magnetoresistance, universal conductance fluctuations of light waves, optical negative temperature coefficient resistance, and Anderson localization of light.
Also known are periodic dielectric structures which behave as semiconductor crystals for light waves. In periodic structures, the interference is constructive in well-defined propagation directions, which leads to Bragg scattering and complete reflection. At high enough refractive index contrast, propagation is prohibited in any direction within a characteristic range of frequencies. This phenomenon is referred to as a photonic band gap in analogy with the electronic band gap in a semiconductor.
For example, so-called “quasicrystals” are nonperiodic structures that are constructed following a simple deterministic generation rule. If made from dielectric material, the resulting structure has fascinating optical properties. Quasicrystals of the Fibonacci type, for instance, exhibit an energy spectrum with pseudo band gaps and separate areas of high field localization. A Fibonacci quasicrystal is a deterministic aperiodic structure that is formed by stacking two different compounds (referred to as A and B) according to a Fibonacci generation scheme: Sj+1={Sj−1Sj} for j>=1, with S0={B} and S1={A}. The lower order sequences are S2={BA}, S3={ABA}, S4={BAABA}, etc.